Charged particles collectively refer to “particles with charges” such as ions that are certain elements in the periodic table in a certain positive or negative charge state, and electrons. Further, the charged particles include particles consisting of a large number of molecules such as compounds or protein.
Synchrotrons include rf synchrotrons and synchrotrons using an induction accelerating cell. An rf synchrotron is a circular accelerator for applying, with an rf acceleration cavity, an rf acceleration voltage synchronized with a magnetic field excitation pattern of a bending magnet that ensures strong focusing of a design orbit along which a charged particle beam circulates to charged particles such as protons injected into a vacuum duct by an injector, and circulating the charged particles along the design orbit in the vacuum duct.
In the rf synchrotron, the injected charged particles in the form of several bunches circulate along the design orbit of the rf synchrotron. When a bunch arrives at the rf acceleration cavity, the bunch receives the rf acceleration voltage synchronized with the magnetic field excitation pattern to be accelerated up to a predetermined energy level.
The bunch refers to a group of charged particles that circulate along the design orbit with phase stability.
A voltage required for acceleration calculated from an inclination (the time rate of change) of the magnetic field excitation pattern of the bending magnet is applied to the bunch as an rf acceleration voltage. The rf acceleration voltage has both the function of supplying the voltage required for accelerating the bunch, and the function of confinement for preventing diffusion of the bunch in an advancing axis direction.
These two functions are essential for accelerating the bunch in the rf synchrotron. The function of confinement is sometimes particularly referred to as phase stability. The phase stability refers to a state in which, by the rf acceleration voltage, individual charged particles receive focusing forces in the advancing axis direction and are formed into a bunch, and circulate in the rf synchrotron while moving forward and backward in the advancing axis direction of the charged particles in the bunch. Time periods are limited in which the rf acceleration voltage has the two functions.
On the other hand, a synchrotron using an induction accelerating cell has a different acceleration principle from the rf synchrotron, and is a circular accelerator for applying an induced voltage to a charged particle beam with the induction accelerating cell for acceleration. FIG. 16 shows an acceleration principle of charged particles by an induction accelerating cell.
FIG. 16 shows the acceleration principle of a charged particle beam by induced voltages applied from conventional induction accelerating cells having different functions. The induction accelerating cells are classified according to their functions into an induction accelerating cell for confinement of charged particle beams in the advancing axis direction (hereinafter referred to as an induction accelerating cell for confinement), and an induction accelerating cell for applying induced voltages for accelerating the charged particle beams in the advancing axis direction (hereinafter referred to as an induction accelerating cell for acceleration).
An rf acceleration cavity may be used for confinement of a bunch 3 in the advancing axis direction instead of the induction accelerating cell for confinement. Thus, conventional acceleration of the charged particle beams using the induced voltages requires the two functions of acceleration and confinement.
FIG. 16(A) shows confinement of the bunch 3 by the induction accelerating cell for confinement. The induced voltages applied to the bunch 3 by the induction accelerating cell for confinement are barrier voltages 17.
Particularly, a barrier voltage 17 applied to a bunch head 3d in a direction opposite to the advancing axis direction of the bunch 3 is a negative barrier voltage 17a, and a voltage value thereof is a negative barrier voltage value 17c. A barrier voltage 17 applied to a bunch tail 3e in the same direction as the advancing axis direction of the bunch 3 is a positive barrier voltage 17b, and a voltage value thereof is a positive barrier voltage value 17d. 
These barrier voltages 17 provide phase stability to the bunch 3 like the conventional radio frequency waves. The axis of abscissa t represents changes with time in the induction accelerating cell for acceleration, and the axis of ordinate v represents an applied barrier voltage value (an induced voltage value for acceleration in FIG. 16(B)).
FIG. 16(B) shows acceleration of the bunch 3 by the induction accelerating cell for acceleration. Induced voltages applied to the bunch 3 by the induction accelerating cell for acceleration are induced voltages for acceleration 18. Particularly, an induced voltage for acceleration 18 applied to the entire bunch 3 from the bunch head 3d to the bunch tail 3e and required for accelerating the bunch 3 in the advancing axis direction is an acceleration voltage 18a, and a voltage value thereof is an acceleration voltage value. A time period when the acceleration voltage 18a is applied is a charging time period 18e. 
An induced voltage for acceleration 18 having a different polarity from the acceleration voltage 18a in a time period when no bunch 3 exists in the induction accelerating cell for acceleration is a reset voltage 18b, and a voltage value thereof is a reset voltage value 18d. The reset voltage 18b avoids magnetic saturation of the induction accelerating cell for acceleration.
It is considered that the barrier voltages 17 and the induced voltages for acceleration 18 allow acceleration of protons, which has been demonstrated as disclosed in “Phys. Rev. Lett. Vol. 94, No. 144801-4 (2005)” as Non-Patent Document 1.
Further, as disclosed in the bulletin of the Physical Society of Japan Vol. 59, No. 9 (2004) p 601-p 610 as Non-Patent Document 2, it is considered that the use of the induction accelerating cell allows acceleration of a bunch 3 (super-bunch) of 1 μsec corresponding to a time width of several to ten times the length of the beam accelerated by the conventional rf synchrotron.
FIG. 17 shows synchrotron oscillation. In the confinement and acceleration methods of the charged particles in the advancing axis direction in the rf synchrotron, it is known that a phase space area in which the bunch 3 can be confined is restricted in principle particularly in the advancing axis direction (time axis direction).
Specifically, in a time area where the radio frequency waves 36 are at a negative voltage, the bunch 3 is reduced in speed, and in a time area with a different polarity of a voltage gradient, the charged particles diffuse in the advancing axis direction and are not confined. In other words, only an acceleration area 36a shown by the double-headed dotted arrow can be used for accelerating the bunch 3.
In the acceleration area 36a, the phase of the radio frequency waves 36 is moved and controlled to apply a center acceleration voltage 3f that is a constant voltage to a bunch center 3c. Thus, the charged particles positioned in the bunch head 3d have higher energy and arrive earlier at the rf acceleration cavity than the bunch center 3c does, and thus receive a lower head acceleration voltage 3g than the center acceleration voltage 3f received in the bunch center 3c and reduce their speed.
On the other hand, the charged particles positioned in the bunch tail 3e have lower energy and arrive later at the rf acceleration cavity than the bunch center 3c does, and thus receive a greater tail acceleration voltage 3h than the center acceleration voltage 3f received in the bunch center 3c and increase their speed. During the acceleration, the charged particles repeat this process.
This is phase stability, and the phase stability, resonance acceleration, and strong focusing are three main principles for allowing synchrotron acceleration of charged particles.
A state where the phase stability is provided to the bunch 3, and the charged particles that constitute the bunch 3 rotate forward and backward in an acceleration direction symmetrically with respect to the bunch center 3c is synchrotron oscillation 3i, and a rotation frequency of the charged particles at the time is a synchrotron oscillation frequency.
The confinement is a function required because the charged particles that constitute the bunch 3 always have variations in kinetic energy. The variations in kinetic energy cause differences in time for the bunch 3 to arrive at the same position after one turn along the design orbit. Without the confinement, the time difference is increased for each turn, and the charged particles diffuse over the entire design orbit.
When positive and negative induced voltages are applied to opposite ends of the bunch 3, energy is transferred to particles delayed in revolution because of insufficient energy by the positive induced voltage, entering an energy excessive state, and energy is lost from charged particles advanced in revolution because of excessive energy by the negative induced voltage, entering an energy insufficient state.
Thus, the particles delayed in revolution are advanced, while the particles advanced in revolution are delayed, thereby allowing the bunch 3 to be localized in a certain area in the advancing axis direction. The series of operations is referred to as the confinement of the bunch 3.
The function of the induction accelerating cell for confinement is thus equal to the separated function of confinement of the conventional rf acceleration cavity.
The devices for confinement have the function of reducing the length of the charged particle beam injected from an injection device into the synchrotron using the induction accelerating cell to be formed into the bunch 3 having a certain length so that the charged particle beam can be accelerated by another induction accelerating cell with a predetermined induced voltage having a different polarity or changing the length of the bunch 3 in various ways, and the function of providing phase stability to the bunch 3 during acceleration.
The devices for acceleration have the function of providing the induced voltage for acceleration 18 to the entire bunch 3 after the formation of the bunch 3.
In the conventional rf synchrotron, a phenomenon is known in which radio frequency waves unpredictable in a design stage are applied to the bunch 3 from devices that constitute the rf synchrotron. This phenomenon is referred to as disturbance. The disturbance is electromagnetic waves generated by the devices that constitute the synchrotron, and applied to the bunch 3 as a constant rf frequency depending on installation states for each acceleration.
When the frequency of the synchrotron oscillation 3i of the bunch 3 matches or becomes integer times the frequency of the disturbance, resonance with the synchrotron oscillation 3i is induced, the charged particles are displaced from ideal energy, and the bunch 3 diffuses in the advancing axis direction, exceeds the time width of the acceleration area 36a of the radio frequency waves 36 and is lost. Similarly, when the induction accelerating cell for acceleration is used for accelerating the charged particle beam, the bunch 3 exceeds the length of the charging time period 18e of the acceleration voltage 18a and is lost.
For example, the charged particles in the bunch head 3d receive the rf acceleration voltage in a direction opposite to the acceleration direction, cannot be synchronized with the magnetic field excitation pattern of the synchrotron, collide with a wall surface of the vacuum duct and are lost.
In the acceleration of the charged particles, the loss of the particles reduces acceleration efficiency, and also causes a significant problem of activation of a spot of the collision with the wall surface of the vacuum duct to no small extent because any charged particles have high energy.
Thus, in conventional acceleration of charged particles, a synchrotron oscillation frequency is controlled by an amplitude changing device that can change the amplitude of radio frequency waves to avoid a match with the frequency of disturbance for preventing loss of charged particles by the disturbance.
Thus, the charged particle beam cannot be actually accelerated by the induced voltage without controlling the synchrotron oscillation frequency.
FIG. 18 shows an example of a forming process of a super-bunch by a conventional induced voltage. For forming the super-bunch 3m, it is necessary to inject the bunch 3 into the vacuum duct multiple times and connect multiple bunches 3.
In FIG. 18(A), a method of injecting the multiple bunches 3, and then connecting a further bunch 3 to a temporally long bunch 3o constituted by the bunches 3 successively connected before acceleration will be described. The super-bunch 3m is formed after the injection of the multiple bunches 3 and before confinement and acceleration of each bunch 3 with the barrier voltages 17.
The negative barrier voltage 17a and the positive barrier voltage 17b are applied to the bunch head 3d and the bunch tail 3e, respectively, of the bunch 3o to perform confinement for each turn. At this time, generation timing of the barrier voltages 17 is constant.
To the bunch 3 to be connected to the bunch 3o, negative and positive barrier voltages 17a and 17b are applied by an induction accelerating cell for movement separate from the induction accelerating cell for confinement, and the bunch 3 is brought close to the bunch 3o while being confined. For bringing the bunch 3 close to the bunch 3o, generation timing of a barrier voltage for movement 17g is gradually advanced.
This shortens a time duration between generations of the barrier voltage 17 used only for confinement and the barrier voltage for movement 17g (hereinafter referred to as a time duration between barrier voltage pulses 17h), and the bunch 3 is brought close to the bunch 3o (in the direction of the open arrow in the drawing) for each turn.
Finally, the positive barrier voltage of the bunch 3o is generated in a position corresponding to the bunch tail 3e of the bunch 3 to integrally connect the bunch 3o and the bunch 3. It has been considered that the super-bunch 3m is thus formed (FIG. 18(B)).
It has been considered that the super-bunch 3m thus formed can be confined by the barrier voltages 17 including the negative barrier voltage 17a and the positive barrier voltage 17b, and accelerated by the induced voltage for acceleration 18 applied from the induction accelerating cell for acceleration separate from the induction accelerating cell for confinement.
However, the conventional acceleration of the charged particle beam by the induced voltage requires combination of induction accelerating cells and devices for controlling generation timing of induced voltages applied by the induction accelerating cells for each function of the induced voltages. For example, required combinations include an induction accelerating cell for acceleration, an induction accelerating cell for confinement, an induction accelerating cell for movement, an induction accelerating cell for synchrotron oscillation frequency control, and an induction accelerating cell for charged particle beam orbit control, and devices for controlling induced voltages applied by the induction accelerating cells.
Thus, each of the induced voltages needs to be controlled, which is complicated. Also, the combinations of the induction accelerating cells having respective functions and the devices for controlling the generation timing of the induced voltages applied by the induction accelerating cells need to be prepared, which increases construction costs of the accelerator.
Thus, the present invention has a first object to provide an induction accelerating cell for controlling acceleration of a charged particle beam and a set of induction accelerating device for controlling generation timing of an induced voltage applied by the induction accelerating cell in a synchrotron.
The present invention has a second object to provide an acceleration method of a charged particle beam by induced voltages having the same pulse shape, by using the induction accelerating device to control generation timing of the induced voltage.
The present invention has a third object to provide an accelerator that can accelerate arbitrary charged particles up to an arbitrary energy level permitted by magnetic field strength of a bending magnet that constitutes a synchrotron using an induction accelerating cell (hereinafter referred to as an arbitrary energy level) with one accelerator, by using the induction accelerating device.